circular motion - universe of ali ovgun · 2018. 8. 28. · lecture 5 circular motion dr. ali...
TRANSCRIPT
Physics 111Lecture 5
Circular MotionDr. Ali ÖVGÜN
EMU Physics Department
www.aovgun.com
January 22, 2017
Multiple Objects
q A block of mass m1 on a rough, horizontal surface is connected to a ball of mass m2 by a lightweight cord over a lightweight, frictionless pulley as shown in figure. A force of magnitude F at an angle θ with the horizontal is applied to the block as shown and the block slides to the right. The coefficient of kinetic friction between the block and surface is μk. Find the magnitude of acceleration of the two objects.
January 22, 2017
Multiple Objectsq m1:
q m2:amamgmTF yy 222 ==−=∑
0sin
cos
1
11
=−+=
==−−=
∑∑
gmFNF
amamTfFF
y
xkx
θ
θ
θsin1 FgmN −=
2 1cos ( )kF f m a g m aθ − − + =
2
1 2
cos kF f m gam mθ − −=
+
)(2 gamT +=
January 22, 2017
Uniform circular motion
Constant speed, or,constant magnitude of velocity
Motion along a circle:Changing direction of velocity
Uniform Circular Motion: Definition
January 22, 2017
Uniform Circular Motion: Observations
q Object moving along a curved path with constant speedn Magnitude of velocity: samen Direction of velocity: changingn Velocity : changingn Acceleration is NOT zero!n Net force acting on an
object is NOT zeron “Centripetal force” amFnet
!!=
v!
January 22, 2017
January 22, 2017
Uniform Circular Motionq Velocity:
n Magnitude: constant vn The direction of the velocity is
tangent to the circleq Acceleration:
n Magnitude: n directed toward the center of
the circle of motionq Period:
n time interval required for one complete revolution of the particle
rvac2
=
rvac2
=
vrT π2=
vac!! ⊥
January 22, 2017
Centripetal Forceq Acceleration:
n Magnitude: n Direction: toward the center of
the circle of motionq Force:
n Start from Newton’s 2nd Law
n Magnitude:
n Direction: toward the center of the circle of motion
rvac2
=
rvac2
=
amFnet!!
=
vac!! ⊥
rmvmaF cnet
2
==
netFr
netFr
netFr
vFnet!!
⊥
netc Fa!! ||
January 22, 2017
What provide Centripetal Force ?
q Centripetal force is not a new kind of forceq Centripetal force stands for any force that keeps
an object following a circular path
q Centripetal force is a combination of n Gravitational force mg: downward to the groundn Normal force N: perpendicular to the surfacen Tension force T: along the cord and away from objectn Static friction force: fs
max = µsN
rmvmaF cc
2
==
January 22, 2017
a
What provide Centripetal Force ?
rmvT
maTFnet2
=
==
rvmmgN
mamgNFnet2
+=
=−=
mg
N
January 22, 2017
Problem Solving Strategyq Draw a free body diagram, showing and labeling all
the forces acting on the object(s)q Choose a coordinate system that has one axis
perpendicular to the circular path and the other axis tangent to the circular path
q Find the net force toward the center of the circular path (this is the force that causes the centripetal acceleration, FC)
q Use Newton’s second lawn The directions will be radial, normal, and tangentialn The acceleration in the radial direction will be the centripetal
accelerationq Solve for the unknown(s)
January 22, 2017
Example 1:The Conical Pendulumq A small ball of mass m is suspended from a string
of length L. The ball revolves with constant speed v in a horizontal circle of radius r. Find an expression for v and a
mg
T θ
44.0tan
4.0sin
sin
cos
0cos 2 5 5
22
2
=−
=
==
===
=
=−====
∑
∑
rLr
Lr
rmvmaTF
mgTmgTF
mrmLkgm
cx
y
θ
θ
θ
θθ
January 22, 2017
The Conical Pendulum
44.0tan
4.0sin
sin
cos
0cos 2 5 5
22
2
=−
=
==
==
=
=−====
∑
∑
rLr
Lr
rmvTF
mgTmgTF
mrmLkgm
x
y
θ
θ
θ
θθ
22
2
2
m/s 3.4tan
m/s 9.2tansin
tan
tan
cos
sin
===
==
=
=
=
=
θ
θθ
θ
θ
θ
θ
grva
Lgv
rgv
grvmgTrmvT
q Find v and a
Example 2: The Effect of Speed on Centripetal Force
q The model airplane has a mass of 0.90 kg and moves at constant speed on a circle that is parallel to the ground. The path of the airplane and the guideline lie in the same horizontal plane because the weight of the plane is balanced by the lift generated by its wings. Find the tension in the 17 m guideline for a speed of 19 m/s.
January 22, 2017
q In vertical circular motion the gravitational force must also be considered. An example of vertical circular motion is thevertical “loop-the-loop” motorcycle stunt. Normally, the motorcycle speed will varyaround the loop.
q The normal force, FN, and the weight of the cycle and rider, mg, are shown at fourlocations around the loop.
January 22, 2017
Vertical Circular Motion
January 22, 2017
qThere is a minimum speed the rider must have at point 3 in order to stay on the loop.
qThis speed may be found by settingin the centripetal force equation or point 3, i.e. in
January 22, 2017
January 22, 2017
Problem 1:
January 22, 2017
Problem 2:
January 22, 2017
Problem 3:
Problem 4:
January 22, 2017
January 22, 2017
Problem 5:
Problem 6:
January 22, 2017
Problem 7: